Finding ratio of perimeter with surrounding neighbors in R

Question

I have a shape file at Sample Data

I read the data in R as sf object named "SD" and have columns "GEOID" and "geometry" along with other columns. I created a new column in the data named "POP"

SD$POP <- sample(2000:8000, 35)

First, I want to measure the area and perimeter for each "GEOID".

Second, I need to find how ratio of each GEOID's perimeter shared with it's surrounding GEOIDs. For example: say GEOID 09 is surrounded by GEOID 06, 08, 10, 13. I want to find what percent of GEOID 09's perimeter is shared with 06, 08, 10, and 13 individually. Then Create new columns "POP_PERCENT" and "ADJ_POP" which will be

ADJ-POP = SUM OF POP for GEOID 06, 08, 10, and 13' .

POP_PERCENT =  Percent share with 06 + Percent share with 08 + Percent share with 10 +
Percent share with 13 

My apologies for verbose question. I would really appreciate any help.